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IBM

MCP Math Server

by IBM

dudeney_numbers

Calculate all Dudeney numbers up to a specified limit. Dudeney numbers are special integers where the sum of their digits equals the cube root of the number.

Instructions

Find all Dudeney numbers up to limit. (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe output format, performance characteristics, error handling, or computational limits. For a tool with no annotations, this is a significant gap in transparency about how it behaves when invoked.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded: the first sentence states the core functionality, and the second adds domain/category context. There's no wasted verbiage, and every word contributes to understanding the tool's purpose efficiently.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's mathematical nature, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what Dudeney numbers are, how results are returned, or any limitations. For a tool that likely generates a list of numbers, more context is needed to use it effectively.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The description mentions the 'limit' parameter, which aligns with the single required parameter in the schema. However, schema description coverage is 0%, and the description doesn't add details like valid ranges, units, or examples. It provides basic semantics but doesn't compensate for the lack of schema documentation, meeting the baseline for minimal parameter information.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Find all Dudeney numbers up to limit.' It specifies the verb ('Find'), resource ('Dudeney numbers'), and scope ('up to limit'). However, it doesn't differentiate from siblings like 'armstrong_numbers' or 'narcissistic_numbers' beyond the domain/category tags, which is why it doesn't reach a perfect 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('special_numbers'), but doesn't specify use cases, prerequisites, or compare it to similar tools like 'armstrong_numbers' or 'happy_numbers' in the sibling list. This leaves the agent with minimal context for tool selection.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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